I got an Interesting number sequence.
It's the' Kolakoski sequence'..
and i'm just going to write it out..
and see if you can see why it might be interesting.
We go, "One"
"Two".
I'm going to put a comma in.
Two, two
One, one
Two...
...
One
Two
Sometimes, I like to call this the Ready
Sequence because it's like: 1 2 2 1 1 2
Testing!
Why is this interesting?
This kit carries over, like this..
There's going to be a pattern there and you might think:
"This is a really boring sequence because it's got one's and two's"
and that's-that's not even in any particular order!
But let's look at the runs, because the numbers..
Either coming in runs of One or Two, interestingly.
So, this is a run of one because it's just one "1".
So...
I'll write a '1'.
Here's a run of '2', because, there are two of them....
and the run of '2'...
Oh, a run of '1', a run of '1'.
Oh, a run of '2'...
and have you noticed something very interesting?
This one starts with 1,2,2,1,1,2.
and here... 1,2,2,1,1,2...
and this will...
Continue forever.
In other words...
"The sequence...
describes...
itself, by...
telling you the length of the run.
It's a very, very famous sequence.
It's one of the very first ones that was put in the...
'Online Encyclopedia of Integer Sequences', so people just say it's the kind of the 'Kolakoski Sequence' and in fact,
there are only two sequences that have this property...
and it's this one...
and, this one.
Which is the 'Kolakoski sequence' without the '1'
So, it begins 2,2,1,1,2,1,2,2...
Brady: Do you know who 'Kolakoski' was?
Bill.
I think he's called 'William''
'William Kolakoski', and I know that...
He came up with this idea in the 1960s.
It's like, you're sort of...
scratching your own back and the other hand's coming there.
It's like a sort of 'Escher' painting
but done in numbers.
So in the book that I did with Edmund Harriss
We, rather 'he did'
I would like to claim credit but I cannot.
He found a way of representing this, in a rather, sort of, beautiful way.
We have the sequence start in the outer circle, so, the inner one is...
Describing The length of Run and obviously that therefore, becomes a continuation of the same sequence...
and then, within it, within it, within it.
so rather than one sequence and then the other one referring to it, you have these kind of
concentric rings of referring, referring, referring, and that's kind of quite interesting, and quite fun and
If you do all the Twos one color and all the Ones another color, say one black or gray and then one white...
and then you get rid of all the numbers
we're going to get rid of all the numbers, then you see it's this kind of quite, striking
Brady: But that's all white, that is.
This is all white, and that's because, it's a colouring book. (Silly Brady...)
Oh.
well, you know, it's a coloring Book but, if I had this, well I do have this,
Well I do have this but if I was 'Not Me' and I was given this, I'm not Sure I would want to color it
in because I think, actually that
what you get from contemplating it without color, and you see how it all fits in, is rather beautiful.
and you're looking at it and you're seeing there are other patterns that you can see, so you've got this, sort-of blob here.
Kind of gets bigger and bigger and bigger because what's happening, is that as
the ring gets smaller it happens further away, so you get this kind of Shift.
Brady: Kolakoski sequence?
Not 'Kowalski', who, wasn't there a 'Primal Scream' did a song about that?
I think, I think, yeah, because he was-he was some famous
Some filming the guy called 'Kowalski' or something like that, anyway, but it was not him!
Of the mathematical things that you might want to investigate in the sequence is, are there more 1's than 2's?
No one knows. That is another unsolved problem.
A bit like the Collatz Conjecture
but, you'll be a lot less famous if you get this one.
Like it, looks like it approaches 50%...
in the limit.
Brady: We don't know.
No, we don't know.
Brady: Greatness awaits.
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